Abstract
We study the relation between \( {\mathcal{W}}_{1+\infty } \) algebra and Arbesfeld-Schiffmann Tsymbaliuk Yangian using the Maulik-Okounkov R-matrix. The central object linking these two pictures is the Miura transformation. Using the results of Nazarov and Sklyanin we find an explicit formula for the mixed R-matrix acting on two Fock spaces associated to two different asymptotic directions of the affine Yangian. Using the free field representation we propose an explicit identification of Arbesfeld-Schiffmann-Tsymbaliuk generators with the generators of Maulik-Okounkov Yangian. In the last part we use the Miura transformation to give a conformal field theoretic construction of conserved quantities and ladder operators in the quantum mechanical rational and trigonometric Calogero-Sutherland models on which a vector representation of the Yangian acts.
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Procházka, T. Instanton R-matrix and \( \mathcal{W} \)-symmetry. J. High Energ. Phys. 2019, 99 (2019). https://doi.org/10.1007/JHEP12(2019)099
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DOI: https://doi.org/10.1007/JHEP12(2019)099